New insights in nonlinear static stability analysis by the FEM

In order to avoid a fully nonlinear analysis to obtain stability limits on nonlinear load-displacement paths, linear eigenvalue problems may be used t o compute estimates of such limits. In this paper an asymptotic approach fo r assessment of the errors resulting from such estimates is presented. Base d on the consistent linearization of the geometrically nonlinear static sta bility criterion - the so-called consistently linearized eigenvalue problem - higher-order estimation functions can be calculated. They are obtained f rom a scalar post-calculation performed after the solution of the eigenprob lem. Different extensions of these higher-order estimation functions are pr esented. An ab initio criterion for the identification of the type of loss of stability (i.e., either bifurcation or limit-point buckling) is presente d.